If the roots of $x^3-k x^2+14 x-8=0$ are in geometric progression,then $k$ is equal to

Let $S_1$ be the sum of areas of the squares whose sides are parallel to the coordinate axes. Let $S_2$ be the sum of areas of the slanted squares as shown in the figure. Then,$\frac{S_1}{S_2}$ is equal to

If $\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}$ $(x \ne 0)$,then $a, b, c, d$ are in

If $y = x^{1/3} \cdot x^{1/9} \cdot x^{1/27} \cdot \dots \infty$,then $y = \dots$

If $a_{1} (>0), a_{2}, a_{3}, a_{4}, a_{5}$ are in a $G$.$P$.,$a_{2} + a_{4} = 2a_{3} + 1$ and $3a_{2} + a_{3} = 2a_{4}$,then $a_{2} + a_{4} + 2a_{5}$ is equal to

The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\frac{27}{19}$. Then the common ratio of this series is